A. The input-output table should be completed as shown below.
B. The type of relation between the figure number and the number of dots in a figure is an arithmetic sequence.
C. Yes, this is a function.
D. This relation is a function because each input value is uniquely mapped to one output value. An algebraic expression that represents the relation is 3n + 2.
By using the figure number (n) as the input and the number of dots (D) as the output, the input-output table should be completed as follows;
Figure number (n input) 1 2 3 4
Number of dots (D output) 5 8 11 14
Part B.
Based on the pattern, we can logically deduce that the figure number and the number of dots represents an arithmetic sequence.
Part C.
Yes, this relation is a function.
Part D.
This relation is a function because each input value is uniquely mapped to one output value. The nth term of this sequence can be calculated as follows;
Common difference, d = succeding term - preceeding term
Common difference, d = 8 - 5 = 11 - 8 = 14 - 11
Common difference, d = 3
f(n) = 5 + (n - 1)3.
f(n) = 5 + 3n - 3
f(n) = 3n + 2